Class 10 Maths Chapter 7 Coordinate Geometry – Exercise 7.2 NCERT Solutions

Introduction

Exercise 7.2 introduces the section formula in coordinate geometry. It helps find the coordinates of a point dividing a line segment internally or externally in a given ratio. This exercise builds the foundation for solving problems involving midpoints, ratios, and geometric constructions using coordinates.

Formula Used

• Section Formula (Internal Division): If point $P(x,y)$ divides line segment joining $A(x_1,y_1)$ and $B(x_2,y_2)$ in ratio $m:n$, then

$$P(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$$

• Midpoint Formula (special case when $m=n$):

$$M(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$$

NCERT Questions with Solutions (10)

Q1. Find coordinates of point dividing line joining (2, 3) and (4, 7) in ratio 1:1.

Solution: Midpoint = $(\frac{2+4}{2},\frac{3+7}{2})=(3,5)$.

Q2. Find coordinates of point dividing line joining (1, 2) and (3, 4) in ratio 2:1.

Solution: $x=\frac{2\cdot 3+1\cdot 1}{3}=\frac{7}{3}$. $y=\frac{2\cdot 4+1\cdot 2}{3}=\frac{10}{3}$. Point = $(\frac{7}{3},\frac{10}{3})$.

Q3. Find coordinates of point dividing line joining (-1, -2) and (3, 6) in ratio 1:3.

Solution: $x=\frac{1\cdot 3+3\cdot (-1)}{4}=\frac{0}{4}=0$. $y=\frac{1\cdot 6+3\cdot (-2)}{4}=0$. Point = (0, 0).

Q4. Find coordinates of point dividing line joining (5, -1) and (-3, 7) in ratio 2:3.

Solution: $x=\frac{2(-3)+3(5)}{5}=\frac{-6+15}{5}=\frac{9}{5}$. $y=\frac{2(7)+3(-1)}{5}=\frac{14-3}{5}=\frac{11}{5}$. Point = $(\frac{9}{5},\frac{11}{5})$.

Q5. Find coordinates of midpoint of line joining (7, 4) and (3, -2).

Solution: Midpoint = $(\frac{7+3}{2},\frac{4+(-2)}{2})=(5,1)$.

Q6. Find coordinates of point dividing line joining (2, -3) and (4, -1) in ratio 3:1.

Solution: $x=\frac{3(4)+1(2)}{4}=\frac{14}{4}=3.5$. $y=\frac{3(-1)+1(-3)}{4}=\frac{-6}{4}=-1.5$. Point = (3.5, -1.5).

Q7. Find coordinates of point dividing line joining (-2, 5) and (6, -3) in ratio 1:1.

Solution: Midpoint = $(\frac{-2+6}{2},\frac{5+(-3)}{2})=(2,1)$.

Q8. Find coordinates of point dividing line joining (0, 0) and (10, 10) in ratio 2:3.

Solution: $x=\frac{2(10)+3(0)}{5}=4$. $y=\frac{2(10)+3(0)}{5}=4$. Point = (4, 4).

Q9. Find coordinates of point dividing line joining (1, -1) and (5, 3) in ratio 1:2.

Solution: $x=\frac{1(5)+2(1)}{3}=\frac{7}{3}$. $y=\frac{1(3)+2(-1)}{3}=\frac{1}{3}$. Point = $(\frac{7}{3},\frac{1}{3})$.

Q10. Find coordinates of midpoint of line joining (-4, -6) and (4, 6).

Solution: Midpoint = $(\frac{-4+4}{2},\frac{-6+6}{2})=(0,0)$.

FAQs (10 from NCERT)

1. Q: What is section formula? A: Formula to find coordinates of point dividing line segment in given ratio.

2. Q: What is midpoint formula? A: Special case of section formula when ratio is 1:1.

3. Q: What is internal division? A: Point lies between two endpoints.

4. Q: What is external division? A: Point lies outside line segment.

5. Q: Can section formula be used for external division? A: Yes, with modified signs.

6. Q: What is ratio m:n? A: Division of line segment into parts proportional to m and n.

7. Q: Can midpoint coordinates be negative? A: Yes, depending on given points.

8. Q: What is Cartesian plane? A: Plane defined by x‑axis and y‑axis.

9. Q: Why is section formula important? A: It helps in geometry, physics, and real‑life problems.

10. Q: Why is this exercise important? A: It builds skills in coordinate geometry and proportional division.

Conclusion

Exercise 7.2 has 10 solved questions and 10 FAQs that strengthen your understanding of the section formula in coordinate geometry. This builds the foundation for advanced topics like centroid, incenter, and equations of lines in Class 10 Maths.

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